1: coralseed theory

Introduction

coralseed is a spatially explicit probabilistic model that attempts to quantify the spatial footprint of coral larval re-seeding from restoration progjects. The model is based on high-resolution oceanographic models (e.g. CONNIE) that allow for tracking of individual particles following release through space and time. By incorporating experimental data on larval behaviour (competency, habitat specific substrate settlement preferences, swimming behaviour) settlement probability can be modelled individually for 105 - 106 larvae. The temporal dispersal-competency model is then overlaid onto high-resolution habitat maps (Allen Coral Atlas) forming a spatially-explicit probabilistic model of settlement following release of coral larvae.

coralseed aims to provide insight into key knowledge gaps in larval restoration: 1) Where do larvae settle following release? 2) What is the spatial footprint of larval reseeding projects? 3) what are the likely densities of settled corals? 4) What densities of adult corals (~10cm size) are produced from reseeding and where are they located? By varying initial model parameters (e.g. tidal currents, time of release, larval competency, larval densities, location of release sites), a simulation modelling approach can be used to quantify the likely spatial footprint and expected settlement densities, allowing for optimisation and upscaling of larval reseeding programs on the Great Barrier Reef and elsewhere.

coralseed model is formed from three main sections:

  1. Probabilistic model of larval competency through time: the model is parameterised on fine-scale (hourly) data on coral settlement from wild-captured larvae cultured from the nGBR. The proportion of larvae settling through time is used to create a Bayesian probabilistic model of coral settlement in the early time period following release (0-12hrs), simulating a larval release on reef substrates.

  2. Individual-based modelling of larval competency from dispersal models: the model leverages a high-resolution particle tracking model (CONNIE 3) that simulates particle releases from a point-source larval re-seeding project at Lizard Island (nGBR) in 2022. The model overlays the temporal trajectories from the probabilistic settlement model on spatial particle tracks to determine likely settlement times across dispersal trajectories.

  3. Quantifying spatial mosaics of coral settlement potential from habitat maps: By combining high-resolution satellite-derived maps of coral habitats adjacent to release sites (https://allencoralatlas.org) with larval behaviour determined from experimental results on settlement preferences and habitat electivity (e.g. reef crest, reef slope), coralseed creates spatially explicit predictions of coral settlement across seascapes.

Below is the full code and data in R for coralseed v0.0.0.9 with a (mostly) complete explanation of how the model functions. coralseed is intended to be flexible in terms of parameterisation, and can be generalised beyond the current implementation. The document is in rmarkdown format (Show / Hide buttons in each code section expand code and details.



### 1. Probabilistic models of larval competency

In larval re-seeding programs, larvae are cultured (either in aquaculture facilities on land or within culture ponds at sea) and held until they reach optimal competency (usually determined by either i) adding n larvae to a tile and quantifying settlement after 10-24hrs, or ii) adding tiles to culture ponds and quantifying the proportion of larvae that settle after a 24hrs. Competency assays are repeated daily, and larvae are then released onto the reef after 3-6 days at peak of competency (i.e. highest number of settled larvae) to maximise the impact of larval reseeding.

coralseed defines competency as the duration of time from release to settlement (from the perspective of larvae at are n days old following fertilisation). This definition differs from traditional studies of larval competency (e.g. Heyward & Negri 1999, Connolly & Baird 2010) and that derive larval competency as the proportion of n larvae settling in a 24hr period across multiple days. The distinction is important as coralseed models competency as continuous (i.e. hourly measurements) individual-based measures within a single cohort, while traditional studies (and dispersal models) define discrete (daily) measures across multiple cohorts.

To parameterise coralseed, we ran several experiments at SeaSims and during coral spawning in the nGBR in 2022. The experiments tracked settlement of replicated cohorts of larvae (n=100 per replicate) at hourly timepoints (either 0 to 48hrs at SeaSims or 0-12hrs with wild spawn). In all experiments, larvae were released into 1 litre aquaria with a preconditioned settlement tile for substrate.

coralseed v0.1 uses the experimental results from wild-captured coral larvae from Lizard Island in Dec 2022. Briefly, five replicate pre-conditioned tiles were placed in individual 1 litre through-flow aquaria (below left) to simulate natural conditions, and 100 larvae added to each container at t0. Tiles were imaged hourly following larval release using a high-resolution camera (Sony a7R IV) and in-water probe lens (Laowa 24mm) between t0-6 hrs and again at ~t10 hrs. The proportion of larvae settling through time was quantified by tracking individual settlement through time (below right).

Experimental results

Quick summary of key results:

  • Initial settlement is rapid and slows at around 2-3hrs.
  • Settlement at 10hrs averaged 10 - 30%
  • Settlement is increasing between 6 and 10hr time points (i.e. not reached an asymptote by 10hrs)
  • Predicted settlement densities at 24hrs averaged ~ 0.9 settlers per cm2 of available substrate

Settlement densities were similar to field experiments after 24hrs (~1.0 settlers per cm2) at Lizard Island in Dec 2022 where 100k larvae were released into 1.5 * 1.5m net enclosures on the reef.


#### Probabilistic approach to determining competency

One approach to modelling time-censored data is survival analysis, which explicitly considers time-to-event outcomes. Applying this to the settlement experiment, survival analysis becomes “time-to-settlement” rather than “time-to-death”. Each experimental time point can be considered as a census of 100-n larvae from the initial starting pool, with individuals undergoing a binary transition where swimming larvae = “0” and settled larvae = “1”. To estimate probability of settlement through time, the data is fit with a Bayesian discrete-time survival model with a Weibull distribution, resulting in posterior distributions for shape and scale that accounts for between-replicate variability in a multilevel framework.

The survival model is fit in brms (see code for details), where the scale and shape parameters are resampled from the posterior draws using scale = exp(mu) / gamma(1 + 1/k). Predictions of time-to-competency for each individual were estimated from the Weibull parameters (shape, scale) using the rweibull function for each of the 10k posterior draws.

The plot below shows the model outputs: probability of settlement from initial release to t12hrs. Thick black line represents the median model output, thin lines represent 100 random draws from the posterior (highlighting variability in predicted trajectories from the multilevel approach).

Predictions for time-to-settlement for parameterising dispersal models (105 - 106 larvae) were obtained from draws from the posterior. The figure below (a) is an example of 100 posterior draws representing the probable time-to-settlement for 100 individual (ordered) particle tracks with the median probability density function of the Weibull fit. For the simulated population of n=100 larvae the model proximates the median fit, predicting 44% competence at t12hrs (56% larvae remain in an incompetent state either to settle at a later stage or undergo mortality).

The same dataset is visualised (below, figure b) as 1-dimensional trajectories of the same population of 100 larvae, where green points indicate the release of larvae at t0, and red points represent the predicted competence time for an individual larvae. Transposing these trajectories onto dispersal tracks, “competence” is used in the context of “competent and able to settle” rather than “settled” in

The trajectories are used to parameterise spatiotemporal trajectories by transposing a binary state (“not competent” vs “competent”) on particle tracks from hydrodynamic models, which rephrases the question “when do larvae become competent?” to “where are larvae in space when they become competent in time?”



2. Individual-based modelling of larval dispersal-competency

The coralseed code leans heavily on sf/lwgeom for processing data and spatially mapping, and tmap to visualise the data (an updated v0.2 replaces tidyverse with data.table to speed things up with large datasets).

The following example is based on a simulated larval release of 1k particles for a 0-6 hour time window (15:00 to 21:00) at Lizard Island, December 2021.

First, the model converts the imports data into sf as a series of points for each individual particle track (id) at 12 minute time-steps from initial release:

#> options:        GeoJSON 
#> Reading layer `OGRGeoJSON' from data source 
#>   `https://www.dropbox.com/s/yj44muabx8z2laf/run_day_11656_lizard_fcst_15_2611_93.json?raw=1' 
#>   using driver `GeoJSON'
#> Simple feature collection with 31000 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XYZ
#> Bounding box:  xmin: 145.4448 ymin: -14.64841 xmax: 145.4568 ymax: -14.63941
#> z_range:       zmin: 1.95 zmax: 1.95
#> Geodetic CRS:  WGS 84

head(particle_points_json)
#> Simple feature collection with 6 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XYZ
#> Bounding box:  xmin: 145.454 ymin: -14.64806 xmax: 145.4543 ymax: -14.64786
#> z_range:       zmin: 1.95 zmax: 1.95
#> Geodetic CRS:  WGS 84
#>   id decay_value                time                       geometry
#> 1  0           1 2021-12-01 01:46:00 POINT Z (145.454 -14.64786 ...
#> 2  0           1 2021-12-01 01:57:00 POINT Z (145.4541 -14.64791...
#> 3  0           1 2021-12-01 02:09:00 POINT Z (145.4542 -14.64795...
#> 4  0           1 2021-12-01 02:21:00 POINT Z (145.4542 -14.64799...
#> 5  0           1 2021-12-01 02:33:00 POINT Z (145.4543 -14.64802...
#> 6  0           1 2021-12-01 02:45:00 POINT Z (145.4543 -14.64806...

coralseed spatially interpolates each particle to 1 minute time-steps across the trajectory and randomly samples from the output of the Bayesian time-to-settlement model to determine a probabilistic competency point (time in minutes following release) for each particle. points are then connected to form paths each particle id according to their competency state through time (either incompetent or competent).

Below is the dispersal time since release (minutes) and larval state for 1000 individual larvae following release. For spatial reference, a “restoratation hectare” boundary (100m x 100m) is overlaid on the centre of the release site (red box).